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Money and Banking

The important assumption that we make is that the variable costs w are fully human ðand borne by individuals in the same groupÞ and therefore proportional to average group incomes. Proposition 1. Assume that w is proportional to average group incomes. Then a. there exists a threshold income y* such that an equiproportionate increase in group incomes that keeps all incomes below y* increases the probability of attack on group members, and b. an equiproportionate increase in the incomes of a group unambiguously lowers attacks instigated by members of that group. Parts a and b represent the two faces of economic fortune. An improvement in the fortunes of a potential victim makes him a more lucrative target, so that violence increases. An improvement in the fortunes of a potential aggressor increases the opportunity cost of engaging in conflict, so that violence decreases. The sign of the correlation between group incomes and subsequent violence tells us something about whether that group contains a preponderance of victims or attackers. To understand how the proposition works, consult figure 2. Consider a potential victim, whose income increases ðin the same proportion as his group’sÞ from y to y0 . The thin downward-sloping line in panel A is the function aðm 2 bÞpðdÞ, which is the expected loss per unit of victim income in the event of an attack. The piecewise-linear segment in that panel is the function cðdÞ 5 minfwd; F * 1 w*dg, deflated by victim income y. The thick nonlinear curve is the sum of these two functions, which our individual seeks to minimize via choice of d. Given that our individual’s income shift mirrors the overall group shift and that w=y is unaffected by group income, there is no change in the sum of the two curves up to some threshold, after which it moves down. This happens because fixed costs are effectively reduced when deflated by rising income, and the ratio of subsequent variable cost w* to income could be reduced as well. The sum of the two functions therefore moves as shown in panel A. However, in this panel, the individual in question has low income, and the capital-intensive technology is not attractive even after the effective fixed cost shifts down. A change in group incomes then has no effect on the optimally chosen defense expenditure of that individual